Disjoint Iterative Chip Equalization and Multi-User Detection for Cdma Communication System on a Mimo Channnel

ABSTRACT

The invention relates to a reception method for communication over frequency-selective channels with a plurality of send antennas and a plurality of receive antennas, to process data received by the receive antennas that, on sending, was successively modulated and spread. To this end, reception uses: 
         first linear filtering ( 202, 202 ′);    first interference subtraction ( 201 ) that uses an estimate of previously regenerated multi-antenna interference (MAI) and intersymbol interference (ISI);    second linear filtering ( 205, 205 ′);    second interference subtraction ( 204 ) that uses an estimate of previously regenerated multi-user interference (MUI); processing to generate an MAI+ISI interference estimate and an MUI interference estimate for the received data from the data filtered in this way. The invention relates further to a reception system adapted to implement the method and a transmission system including the reception system.

GENERAL TECHNICAL FIELD

The present invention relates to the field of digital communications. Itconcerns how to decode efficiently digital data transmitted on afrequency -selective MIMO channel at the same time as optimizing theperformance/complexity trade-off. FIG. 1 shows an overall method oftransmission on a frequency-selective MIMO channel 300 between a sender100 with T send antennas, delivering signals x[n] at the time n, and areceiver 200 with R receive antennas, receiving signals y[n] at the timen.

GENERAL DESCRIPTION OF THE PRIOR ART

Any communications system managing the access of multiple users to thesame channel by allocating specific spreading codes (CDMA) is limited incapacity by multi-user interference (MUI) between users. In the contextof the present invention, transmission is envisaged on a channel liableto generate other kinds of interference such as spatial multi-antennainterference (MAI) caused by multiple send antennas and intersymbolinterference (ISI) caused by the frequency selectivity of the channel.On reception, these various kinds of interference are cumulative andmake recovering the useful information difficult.

Pioneering work carried out by S. Verdu in the 1980s clearlydemonstrated the benefit of exploiting the structural properties ofmulti-user interference (MUI), multi-antenna interference (MAI) andintersymbol interference (ISI) to improve performance for a fixed load(the number of users per chip) or to improve the load for fixedperformance.

Many types of linear detectors have been studied, capable of supportinga greater or lesser load, which load may be evaluated analytically underasymptotic conditions. Without recourse to iterative techniques, theperformance of these detectors falls far short of the performance of amaximum likelihood (ML) detector (for a system with or without coding).

The class of non-linear LIC-ID detectors based on linear iterativecancellation of the interference thus offers an excellent trade-offbetween performance and complexity. LIC-ID detectors use the followingfunctions: linear filtering, weighted regeneration of interference(regardless of its nature), subtraction of the regenerated interferencefrom the received signal. They deliver decisions on the sent modulateddata (or symbols) with a reliability that increases in monotonousfashion with each new attempt. LIC-ID detectors which are intended toeliminate ISI (at block level) asymptotically achieve the performance ofan optimum ML detector with a computation complexity similar to that ofa linear equalizer. LIC-ID detectors intended to combat MUI approximatethe performance of the optimum ML detector with a computation complexitycomparable to that of a simple linear detector.

A remarkable feature of LIC-ID detectors is that they can easily becombined with hard or weighted decisions delivered by the channeldecoder, thus effecting separate and iterative detection and decoding ofthe data.

For CDMA systems that are overloaded (by hypothesis by MUI) transmittingon frequency-selective MIMO channels, the level of interference is suchthat using LIC-ID receivers proves essential. If an iterative strategyis selected, the complexity of the receivers can be reduced, andrendered reasonable, only by simplifying the iterative processing asmuch as possible. LIC-ID detectors are treated separately for ISI andfor MUI in reference [1] (see below) and in the case of ISI+MUI inreference [2] (see below).

-   [1] A. M. Chan, G. W. Wornell, “A New Class of Efficient    Block-Iterative Interference Cancellation Techniques for Digital    Communication Receivers”,IEEE J. VLSI Signal Processing (Special    Issue on Signal Processing for Wireless Communication Systems), vol.    30, pp. 197-215, January-March 2002.-   [2] W. Wang, V. H. Poor, “Iterative (Turbo) Soft Interference    Cancellation and Decoding for Coded CDMA”, IEEE Trans. Commun., vol.    COM-47, no. 9, pp. 2356-2374, September 1999.

Their generalization to MUI+MAI+ISI still constitutes an open subject ofresearch, in particular because of the complexity of the processing tobe effected, implying computations on particularly large matrices.

If a hypothesis of orthogonality exists between the various users onsending, one tempting approach is to re-establish orthogonality at thechip level before any attempt at multi-user detection. Optimummulti-user detection then amounts to a bank of filters matched to eachuser. This approach, developed in document [3] (see below) for anon-overloaded CDMA communications model transmitting on afrequency-selective SISO channel, proves to be the optimum when aperiodic spreading is considered, for example.

-   [3] M. Lenardi, D. T. Slock, “A Rake Receiver with Intracell    Interference Cancellation for DS-CDMA Synchronous Downlink with    Orthogonal Codes,” IEEE VTC, pp. 430-434, 2000.

The present invention goes beyond the framework of the above referenceby considering an overloaded CDMA communications model transmitting on afrequency-selective MIMO channel.

SUMMARY OF THE INVENTION

A first aspect of the invention proposes a receiving method according toany one of claims 1 to 21.

A second aspect of the invention proposes a transmission systemaccording to claim 22.

A third aspect of the invention proposes a receiving method according toany one of claims 23 to 33.

An object of the present invention is to propose a receiver for“multicode” CDMA transmission (K>T) and/or overloaded CDMA transmission(K potential users or streams, spreading factor N<K) onfrequency-selective MIMO channels (T send antennas and R receiveantennas), on the general assumption of there being no CSI (i.e. noinformation as to the state of the channel) at the sender and a perfectknowledge of the CSI at the receiver. The receiver is based on acombination of simple mechanisms and techniques to obtain the bestpossible quality of service at fixed spectral efficiency andsignal-to-noise ratio (SNR) or the best possible usable bit rate atfixed quality of service, band and SNR.

To this end, the invention proposes a device comprising:

-   -   Means for guaranteeing temporal decorrelation of samples of        noise affecting the chips when the multiple access model with K        potential users is reformed on reception assuming the absence of        MAI+ISI, said means comprising chip interleaving before        transmission over the MIMO channel or a periodic spreading. Note        that although chip interleaving is not necessary for internal        linear a periodic coding, it remains an option.

The invention proposes an equalization and iterative decoding deviceincluding a data detector receiving the data coming from the varioussend antennas comprising:

-   -   first linear filtering processing for each send antenna the        MAI+ISI interference and generating statistics on the chips sent        using the spatial diversity offered by the R receive antennas;    -   means for subtracting, before or after any linear filtering        associated with each send antenna, from the received signal the        MAI+ISI interference regenerated for that antenna from the        available estimates of the sent modulated data (or symbolic        data);    -   means for reordering the equalized chips into a multiple access        system with K potential users in which the additive noise        affecting the various chips is assumed to be Gaussian white        noise;    -   second linear filtering processing the MUI interference on the        basis of the chips previously equalized and reordered and        generating statistics on the symbolic data sent by each of the K        potential users;    -   means for subtracting, before or after any linear filtering for        each user, from the observed signal the MUI interference        regenerated for that user from available estimates of the        symbolic data sent;    -   means for processing these statistics and generating        probabilistic bit information usable for external decoding;    -   external decoding with weighted inputs and outputs, capable of        generating probabilistic information referred to as extrinsic        information, pertinent for the calculation of the estimates of        the sent symbolic data (in the sense of the criterion of        minimizing the mean square error (MMSE));    -   means for recursively concatenating the output of the external        decoder both with the MAI+ISI interference regenerator, and with        the MUI interference regenerator.

DESCRIPTION OF THE DRAWINGS

Other features and advantages of the invention will emerge from thefollowing description, which is purely illustrative and non-limiting andshould be read with reference to the appended drawings in which:

FIG. 1 illustrates a general concept of transmission on afrequency-selective MIMO channel;

FIG. 2 shows a first part of a sending process, including externalchannel coding of digital information, interleaving, and demultiplexinginto K streams (one for each potential user);

FIG. 3 shows the second part of the FIG. 2 sending process, includinginternal linear coding corresponding to a periodic space-time(space-frequency) spreading followed by multiplexing onto the T sendantennas;

FIG. 4 shows a second portion of the FIG. 2 sending method, includinginternal linear coding corresponding to a periodic space-time (orspace-frequency) spreading, multiplexing onto a single channel,interleaving at chip level, and demultiplexing to the T send antennas;

FIG. 5 shows a first part of a variant of a sending method includingexternal channel coding of digital information, interleaving, firstdemultiplexing (space demultiplexing) into T streams followed by seconddemultiplexing (code demultiplexing) into U streams;

FIG. 6 shows the second part of the FIG. 5 sending method, including aperiodic time (or frequency) spreading and independent multiplexing foreach antenna, compatible with the UMTS HSDPA mode;

FIG. 7 shows a second portion of the FIG. 4 sending method, including aperiodic time (or frequency) spreading followed by multiplexing onto asingle channel and interleaving at the chip level, followed bydemultiplexing to the T send antennas, compatible with the UMTS HSDPAmode;

FIG. 8 shows a flat ergodic or block level fading equivalent channelobtained by decomposition of the frequency-selective MIMO channel intothe Fourier base and routinely used as a model for multicarriermodulations;

FIGS. 9 and 10 respectively show first and second variants of thearchitecture of a first portion of an LIC-ID receiver of the invention,in which only the functional units necessary for understanding thealgorithm are indicated; FIG. 9 relates to a sending scheme according toFIGS. 2-4 and 5-7 and FIG. 10 relates to the sending scheme describedwith reference to FIGS. 2-3 and 5-6;

FIGS. 11 a and 11 b represent two equivalent methods of implementingLIC-ID receivers for processing MAI+ISI interference, the FIG. 11 aimplementation method representing the filtering and MAI+ISIinterference regeneration parts of the first part of the overalldetector shown in FIG. 9 or FIG. 10.

FIGS. 12 a and 12 b represent two equivalent methods of implementingLIC-ID receivers for processing MUI interference, the implementationmethod of FIG. 12 a representing the filtering and MUI interferenceregeneration parts of the first part of the overall detector shown inFIG. 9 or FIG. 10;

FIG. 13 shows the architecture of the second part of the LIC-ID receiveraccording to the invention (the first portion of the detector beingrepresented by FIG. 9 or FIG. 10), in which only the functional unitsnecessary for understanding the algorithm are indicated.

DESCRIPTION OF PREFERRED EMBODIMENTS OF THE PRESENT INVENTION

1. General Structure of the Sender

Reception is intimately linked to the sending mode, which can be definedby a modulation/coding scheme of high spectral efficiency, and highadaptability capacity, based on the use of spread spectrum modulationand on the use of multiple send and receive antennas. The proposedsolution is pertinent assuming no knowledge of the send channel (no CSI)and a perfect knowledge of the receive channel (CSI). The communicationsmodel is briefly described below in order to introduce a thirdembodiment of the present invention.

Referring to FIG. 2 and FIG. 5, the useful digital data is collected andgrouped into a message m of K_(o) bits constituting the send digitaldata source 101. In each message m, a linear external code C_(o) havingan N_(o)×K_(o) generator matrix G_(o) and constructed on F₂ assigns at102 a code word v of length N_(o) bits defined by the matrix equation:v=G_(o)m

The external coding yield is: $\rho = \frac{K_{o}}{N_{o}}$

The length No of the code words is linked to the various parameters ofthe system by the equation:N _(o) =K×L×qin which K designates the total number of potential users, L the lengthof the packets (in symbol times) and q the number of bits per modulationsymbol. The code may be of any type, for example a convolutional code, aturbocode, an LDPC code, etc. In a multiple access type configuration,the message m consists in a plurality of multiplexed messages fromdifferent sources. Coding is effected independently on each componentmessage. The code word v results from the concatenation 103 of thevarious code words produced.

The code word v is sent to an interleaver 104 operating at the bit leveland, where appropriate, having a particular structure. In a multipleaccess type configuration, the interleaving acts piece by piece on thevarious code words placed one after the other. The output of thisinterleaver is broken up into KL sets of q bits called integers.

The stream of integers is demultiplexed 105 onto K separate channels,where K may be chosen arbitrarily to be strictly greater than the numberT of send antennas. The output from this operation is a K×L integermatrix D. The L columns d[n] n=0, . . . , L−1 of this matrix D have thefollowing structure: ${d\lbrack n\rbrack} = {\begin{bmatrix}{d_{1}\lbrack n\rbrack}^{T} & {d_{2}\lbrack n\rbrack}^{T} & \cdots & {d_{K}\lbrack n\rbrack}^{T}\end{bmatrix}^{T} \in F_{2}^{qK}}$in which the component integers d_(k) [n] k=1, . . . , K are themselvesstructured as follows:d_(k)[n]=[d_(k,1)[n]d_(k,2)[n]. . . d_(k,q)[n]]∈F₂ ^(q)

Referring to FIG. 3, 4, 6, or 7, the integers d_(k) [n] of the matrix Dare then individually modulated 107 via a modulation table μ: F₂ ^(q)

ℑ to yield modulated data, or more precisely complex symbols s_(k)[n] ofa constellation ℑ⊂□ with Q=2^(q) elements. This transforms the integermatrix D into a K×L complex matrix S the L columns s[n] n =0, . . . ,L−1 whereof are structured as follows:s[n]□μ(d[n])=[s ₁ [n]S ₂ [n]. . . S _(K) [n ]] ^(T)∈ℑ^(K)

It is useful to specify the following inverse relationships:μ⁻¹(s[n])□d[n]μ⁻¹(S_(k)[n])□d_(k)[n]μ_(j) ³¹ ¹(S_(k)[n])□d_(k,j)[n]This is followed by internal linear coding (or spreading) of the data.There are several options as to the definition of the generator matrix Wof the internal linear coding (more precisely: generator matrix of theinternal linear coding on the body of the complexes) that may impact onthe structure of the sender and on the characteristics of the linearfront-ends on reception.

-   -   Periodic spreading (or internal linear coding) where W is used        again in each symbol time. To guarantee temporal decorrelation        of the samples of noise affecting the chips when the multiple        access system is reformed after equalization, chip interleaving        must be applied before transmission over the MIMO channel;    -   A periodic spreading (or internal linear coding) where W_(n)        depends explicitly on the symbol time. A periodic spreading        guarantees temporal decorrelation of the samples of noise        affecting the chips when the multiple access system is reformed        after equalization. Chip interleaving is no longer necessary but        remains an option.

Moreover, the spreading may be space-time (or space-frequency) spreadingor only time (or frequency) spreading if it is effected independentlyfor each antenna.

1.1 Space-Time (or Space-Frequency) Spreading (or Internal LinearCoding) Under Overload Conditions

Referring to FIG. 3 or FIG. 4, it is assumed here that a periodicspace-time (or space-frequency) spreading is effected.

The space-time (or space-frequency) spreading is effected for eachmatrix S by means of an N×K internal coding matrix W_(n) which isdenoted W in the periodic context), where:N=T×S _(F) S _(F)∈□

This generator matrix is also called a spreading matrix. For example,this matrix may be considered to be constructed from N orthogonalspreading codes with spreading factor N. This internal linear codingtherefore corresponds, in this case, to space-time (space-frequency)spreading with spreading factor N. The internal coding yield (or load)of the system is the ratio: $\alpha = \frac{K}{N}$

The multiplication at 108 of the symbol vectors s[n] by the generatormatrix W_(n) produces a vector:z[n]□W_(n)s[n]=[z₁[n]z₂[n] . . . z_(N)[n]]^(T)∈□^(N)The relationship may also be written at the matrix level:Z□W_(n)S∈□^(N×L)1.1.1 Spreading Followed by Chip Interleaving

Chip interleaving is necessary if the spreading is periodic (W=W,) inorder to be able (afterwards) to implement reception in accordance withthe invention.

Referring to FIG. 4, the chip vectors z[n] n=0, . . . , L−1 aremultiplexed at 109 into a single stream of chips. The chip stream thendrives a chip interleaver 110, the output whereof is demultiplexed at111 into T separate chip streams (one for each send antenna). The effectof this operation is to transform the N×L chip matrix Z:Z=[z[0]z[1] . . . z[L−1]]∈□^(N×L)into a T×LS_(F) chip matrix X:X=[x[0]x[1] . . . x[LS _(F)−1]]∈□^(T×LS) ^(F)the columns x[l] l=0, . . . , LS_(F)−1 whereof constitute the inputs ofthe MIMO channel:x[l]=[x_(l)[l]x₂[l] . . . x_(T)[l]]^(T)∈□^(T)1.1.2 Spreading not Followed by Chip Interleaving

Referring to FIG. 3, the chip vectors z[n] n=0, . . . , L−1 aredemultiplexed into T separate chip streams (111, one for each sendantenna). The effect of this operation is to transform the N×L chipmatrix Z:Z=[z[0]z[1] . . . z[L−1]]∈□^(N×L)into a T×LS_(F) chip matrix X:X=[x[0]x[1] . . . x[LS _(F)−1]]∈□^(T×LS) ^(F)the columns x[l] l=0, . . . , LS_(F)−1 whereof constitute the inputs ofthe MIMO channel:x[l]=[x_(l)[l]x₂[l] . . . x_(T)[l]]^(T)∈□^(T)1.2 Time (or Frequency) Spreading (Internal Linear Coding)

In this variant of the invention, shown in FIG. 6 or FIG. 7, compatiblewith the HSDPA mode of the UMTS standard, there are S_(F) orthogonalcodes of length S_(F).

The parameter N is always a multiple of T:N=T×S _(F)S_(F)∈□

The S_(F) available codes are re-used at each send antenna (this is thecode re-use principle). The spreading, effected independently for eachantenna, is periodic or a periodic time (or frequency) spreading (W=W,in the periodic context).

This imposes that K be also a multiple of T:K=T×U U∈□This condition, which is not limiting on the invention, yields a newexpression for the internal coding yield (load):$\alpha = \frac{U}{S_{F}}$The generator matrix W_(n) has a block diagonal structure:$W_{n} = {\begin{bmatrix}W_{n}^{(1)} & \quad & \quad & 0 \\\quad & W_{n}^{(2)} & \quad & \quad \\\quad & \quad & ⋰ & \quad \\0 & \quad & \quad & W_{n}^{(T)}\end{bmatrix} \in \bullet^{N \times K}}$the block W_(n) ^((t)) of the generator matrix being associated with theantenna t with dimension S_(F)×U.

Referring to FIG. 5, the integer vector d[n] (demultiplexed at 105,after being coded at 102 and interleaved at 104) sent at the time n hasthe following particular structure:d[n]=[d⁽¹⁾[n]^(T)d ⁽²⁾[n]^(T) . . . d ^((T))[n]^(T)∈F₂ ^(qk)in which the symbol vectors d^((T))[n] t=1, . . . , T are themselvesdefined as follows:d^((t))[n]=[d₁ ^((t))[n]^(T)d₂ ^((t))[n]^(T) . . . d _(U)^((t))[n]^(T)]^(T)∈F₂ ^(qU)

Referring to FIG. 5, the modulation 107 of this multiplexed data d[n]yields a modulated data (or symbols) vector sent at the time n havingthe following particular structure:s[n]=[s⁽¹⁾[n]^(T)S⁽²⁾[n]^(T). . . S^((T))[n]^(T)]^(T)]∈□^(K)in which the symbol vectors s^((t)[n] t=)1, . . . , T are themselvesdefined as follows:s^((T))[n]=[s₁ ^((t))[n]s₂ ^((t))[n] . . . s_(U) ^((t))[n]]^(T)∈□^(U)

The multiplication 108 of the symbol vector s[n] by the generator matrixW_(n) produces the vector:z[n]□W_(n)s[n]which also has a particular structure:z[n]=[z⁽¹⁾[n]^(T)z⁽²⁾[n]^(T). . . z^((T))[n]^(T)]^(T)∈□^(N)in which the chip vectors z^((t)) [n] t=1, . . . , T are themselvesdefined as follows:z^((t))[n]□W_(n) ^((t))s^((t))[n]=[z^((t))[n]z₂ ^((t))[n] . . . Z_(S)_(F) ^((t))[n]]^(T)∈□^(S) ^(F)1.2.1 Spreading Followed by Chip Interleaving

Chip interleaving is necessary if the spreading is periodic (W=W_(n)) inorder to be able (afterwards) to implement reception in accordance withthe invention.

Referring to FIG. 7, the chip vectors z[n] n=0, . . . , L−1 aremultiplexed at 109 into a single stream of chips. The chip stream thendrives a chip interleaver 110, the output whereof is demultiplexed at111 into T separate chip streams (one for each send antenna). The effectof this operation is to transform the N×L chip matrix Z:Z=[z[0]z[1] . . . z[L−1]]∈□^(N×L)into a T×LS_(F) chip matrix X:X=[x[0]x[1] . . . x[LS _(F)−1]]∈□^(T×LS) ^(F)the columns x[l] l=0 . . . , LS_(F)−1 whereof constitute the inputs ofthe MIMO channel:x[l]=[x₁[l]x₂[l] . . . x_(T)[l]]^(T)∈□^(T)1.2.2 Spreading not Followed by Chip Interleaving

Referring to FIG. 6, the chip vectors z^((t)) [n] are then multiplexedat 109-t onto the send antenna t.

It will be noted that, in this sending variant, the recovery of thespatial diversity is effected via the code G₀ (at 102) and external bitinterleaving (at 104). The overload capacity, which is known to increasewith the length of the spreading codes, is lower.

The sending method fits naturally into the general class of space-timecodes. The spectral efficiency of the system (in bits per use of thechannel), assuming a limited band ideal Nyquist filter, is equal to:η=T×ρ _(o) ×q×α

In practice, the send shaping filter has a non-null overflow factor(roll-off) ε. At the receiver, a filter matched to this send filtercould be used for all the receive antennas. It is assumed that thechannel estimation and timing and carrier synchronization functions areimplemented so that the coefficients of the impulse response of thechannel are regularly spaced by an amount equal to the chip time(channel equivalent in the discrete baseband to the discrete time). Thishypothesis is legitimate, the Shannon sampling theorem imposing samplingat the rate (1+ε)/T_(c) which may be approximated by 1/T_(c) when εissmall. Direct generalization is possible for expressions given below fora sampling rate equal to a multiple of 1/T_(c).

2. Channel Model

Transmission is effected on a frequency-selective B-block channel withmultiple inputs and multiple outputs (MIMO):H□{H⁽¹⁾, H⁽²⁾ , . . . , H^((B))}

The channel H^((b)) is assumed constant over L_(x) chips with theconvention:L×S _(F) =B×L _(x) B∈□

The chip matrix X may be segmented into B separate T×L_(x) chip matricesX⁽¹⁾, . . . , X^((B)) (padded on the right and left with physical zerosor guard times if necessary), each matrix X^((b)) seeing the channelH^((b)).

The extreme cases of the B-block model are as follows:

-   -   B=1 and L_(X)=LS_(F)        L_(s)=L quasi-static model    -   B=LS_(F) and L_(x)=1        L_(s)=1 ergodic (chip) model

A renumbering of the chips is applied within each block.

2.1 Convolutional Channel Model

For any block index b, the discrete time baseband equivalent channelmodel (chip timing) is used to write the receive vector y^((b))[l]∈^(R)at the chip time 1 in the form:${y^{(b)}\lbrack l\rbrack} = {{\sum\limits_{p = 0}^{P - 1}{H_{p}^{(b)}{x^{(b)}\lbrack {l - p} \rbrack}}} + {v^{(b)}\lbrack l\rbrack}}$where P is the constraint length of the channel (in chips),x^((b))[l]∈□^(T) is the complex vector of T chips sent at the chip time1, where H_(p) ^((b))□^(R×T) is the matrix coefficient indexed p of theimpulse response of the block MIMO channel indexed b, andv^((b))[l]∈□^(R) is the complex additive noise vector. The complexadditive noise vectors v^((b))[l] are assumed to be independent andidentically distributed in accordance with an R-dimensional Gaussian lawof circular symmetry with zero mean and covariance matrix σ²I. The Pcoefficients of the impulse response are R×T complex matrices, theinputs of which are identically distributed independent Gaussian inputs,with zero mean and with a covariance matrix satisfying the global powernormalization constraint:${E\lbrack {{diag}\{ {\sum\limits_{p = 0}^{P - 1}{H_{p}^{(b)}H_{p}^{{(b)}\dagger}}} \}} \rbrack} = {T\quad I}$in the case of a system with power equally distributed between the sendantennas. Given these hypotheses, the eigen values of the correlationmatrices of the coefficients of the MIMO channel conform to a Wishartdistribution. It is emphasized that equal distribution of the power tothe send antennas is a legitimate power allocation policy in the case ofan absence of knowledge of the sending channel (no CSI).2.2 Block matrix channel model

To introduce the data decoding algorithm, we must show a matrix systemon the set of the type:y ^((b)) =H ^((b)) X ^((b)) +V ^((b))where: ${{\underset{\_}{y}}^{b}\quad{\bullet\quad\begin{bmatrix}{y^{(b)}\lbrack {L_{X} - 1 + P - 1} \rbrack}^{T} & {y^{(b)}\lbrack {L_{X} - 2 + P - 1} \rbrack}^{T} & \cdots & {y^{(b)}\lbrack 0\rbrack}^{T}\end{bmatrix}}^{T}} \in \bullet^{{({L_{x} + P - 1})}\quad R}$${{\underset{\_}{v}}^{b}\quad{\bullet\quad\begin{bmatrix}{v^{(b)}\lbrack {L_{X} - 1 + P - 1} \rbrack}^{T} & {v^{(b)}\lbrack {L_{X} - 2 + P - 1} \rbrack}^{T} & \cdots & {v^{(b)}\lbrack 0\rbrack}^{T}\end{bmatrix}}^{T}} \in \bullet^{{({L_{x} + P - 1})}\quad R}$${{\underset{\_}{x}}^{b}\quad{\bullet\quad\begin{bmatrix}{x^{(b)}\lbrack {L_{X} - 1} \rbrack}^{T} & {x^{(b)}\lbrack {L_{X} - 2} \rbrack}^{T} & \cdots & {x^{(b)}\lbrack 0\rbrack}^{T}\end{bmatrix}}^{T}} \in \bullet^{L_{x}T}$and where H ^((b)) is the Sylvester matrix for the channel:${\underset{\underset{\_}{\_}}{H}}^{(b)} = {\begin{bmatrix}H_{P - 1}^{(b)} & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad \\H_{P - 2}^{(b)} & H_{P - 1}^{(b)} & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad \\\quad & \quad & ⋰ & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad \\\quad & \quad & \quad & H_{0}^{(b)} & H_{1}^{(b)} & \cdots & H_{P - 1}^{(b)} & \quad & \quad & \quad & \quad & \quad & \quad \\\quad & \quad & \quad & \quad & H_{0}^{(b)} & H_{1}^{(b)} & \cdots & H_{P - 1}^{(b)} & \quad & \quad & \quad & \quad & \quad \\\quad & \quad & \quad & \quad & \quad & ⋰ & ⋰ & ⋰ & ⋰ & \quad & \quad & \quad & \quad \\\quad & \quad & \quad & \quad & \quad & \quad & H_{0}^{(b)} & H_{1}^{(b)} & \cdots & H_{P - 1}^{(b)} & \quad & \quad & \quad \\\quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & ⋰ & \quad & \quad \\\quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & H_{0}^{(b)} & H_{1}^{(b)} \\\quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & \quad & H_{0}^{(b)}\end{bmatrix} \in \bullet^{{({L_{S} + M})}{RS}_{F} \times L_{S}{TS}_{F}}}$2.3 Sliding window matrix channel model

In practice, to reduce the dimensions, a sliding window model is used oflength:L _(W) =L ₁ +L ₂+1□L _(s)

The following new system is obtained:Y ^((b)) [n]=H ^((b)) x ^((b)) [n]+V ^((b)) [n]where: ${{\underset{\_}{y}}^{(b)}\lbrack l\rbrack} = {\begin{bmatrix}{y^{(b)}\lbrack {l + L_{1}} \rbrack}^{T} & \cdots & {\quad{y^{(b)}\lbrack {l - L_{2}} \rbrack}^{T}}\end{bmatrix}^{T} \in \bullet^{L_{W}R}}$${{\underset{\_}{x}}^{(b)}\lbrack\quad l\rbrack} = \quad{\begin{bmatrix}{x^{(b)}\lbrack {l + L_{1}} \rbrack}^{T} & \cdots & {\quad{x^{(b)}\lbrack {l - L_{2} - P + 1} \rbrack}^{T}}\end{bmatrix}^{T} \in \quad\bullet^{{({L_{W} + P - 1})}T}}$${{\underset{\_}{v}}^{(b)}\lbrack l\rbrack} = {\begin{bmatrix}{v^{(b)}\lbrack {l + L_{1}} \rbrack}^{T} & \cdots & {\quad{v^{(b)}\lbrack {l - L_{2}} \rbrack}^{T}}\end{bmatrix}^{T} \in \bullet^{L_{W}R}}$and where H(b)is the Sylvester matrix for the channel 300:${\underset{=}{H}}^{(b)} = {\begin{bmatrix}H_{0}^{(b)} & H_{1}^{(b)} & \cdots & H_{P - 1}^{(b)} & \quad & \quad & \quad \\\quad & H_{0}^{(b)} & H_{1}^{(b)} & \cdots & H_{P - 1}^{(b)} & \quad & \quad \\\quad & \quad & ⋰ & ⋰ & ⋰ & ⋰ & \quad \\\quad & \quad & \quad & H_{0}^{(b)} & H_{1}^{(b)} & \cdots & H_{P - 1}^{(b)}\end{bmatrix} \in \bullet^{L_{W}{{RS}_{F} \times {({L_{W} + M})}}{TS}_{F}}}$3. Multipath MIMO Channel Single-Carrier Transmission (HSDPA)

It is assumed here that the bit rate is very high and that the coherencetime of the channel is long, so that L_(X) □ S_(F). For the HSDPA modeof the UMTS standard, the channel is quasi-static, i.e. B=1.

4. Multipath MIMO Channel Multicarrier Transmission (MC-CDMA)

The spreading (or internal linear coding) is space-frequency spreadingor frequency spreading. With reference to FIG. 8, it is well known tothe person skilled in the art that the introduction of a send IFFT 120and a receive FFT 220 yields (ignoring interleaving) an equivalentchannel that is not frequency selective (channel modeled by acirculating matrix using cyclic prefixes, then rendered diagonal in theFourier base). Accordingly, each carrier sees a flat MIMO channel. Usingthe formalism previously described, the channel after FFT may be seen asa non-selective B-block channel (P=1). The width of the sliding windowfor calculating the filters is L_(w=)1.

5. General Structure of The Receiver 200

The iterative receiver 200 is divided into successive interferencecancellation stages. A first stage cancels MAI+ISI interference at chiplevel and attempts to re-establish orthogonality within groups of usersover all the antennas. The second stage cancels MUI interference onceorthogonality has been re-established within the groups of users. Thetwo stages are activated several times. Given the scale of the problem,only linear approaches based on Wiener filters (MMSE criterion) orsimple (single-user) matched filters are envisaged. In both cases, aweighted version of the interference is removed before or afterfiltering.

5.1 Sent Symbol MMSE Estimation

On any iteration i, there is assumed an a priori knowledge of the dataexpressed via logarithmic ratios on the bits of the sent symbols (alsoreferred to as modulated data):${\pi_{k,j}^{i}\lbrack n\rbrack}\bullet\quad\ln\quad\frac{\Pr^{i}\lbrack {{d_{k,j}\lbrack n\rbrack} = 1} \rbrack}{\Pr^{i}\lbrack {{d_{k,j}\lbrack n\rbrack} = 0} \rbrack}$

By convention, these ratios have the value 0 on the first iteration.

Referring to FIG. 9 or FIG. 10, on the basis of this a prioriinformation, there can be found at 212 the matrix S ^(i) of theestimates, in the sense of the MMSE criterion, of the symbols s_(k)[n]sent by the users k=1, . . . , K at the times n=0, . . . , L−1. Theestimate of a symbol is expressed as follows:${{\overset{\_}{s}}_{k}^{i}\lbrack n\rbrack}\bullet{\sum\limits_{s\quad{\varepsilon\mathcal{J}}}^{\quad}\quad{s \times {\Pr^{i}\lbrack {{s_{k}\lbrack n\rbrack} = s} \rbrack}}}$

With deep space-time interleaving, the a priori probability for a symbolmay be approximated by the product of the marginal probabilities of thebits that constitute it:${\Pr^{i}\lbrack {{s_{k}\lbrack n\rbrack} = s} \rbrack} \approx {\prod\limits_{j = 1}^{q}\quad{\Pr^{i}\lbrack {{d_{k,j}\lbrack n\rbrack} = {\mu_{j}^{- 1}(s)}} \rbrack}}$equality being obtained for an infinite interleaving depth.

To introduce the logarithmic ratio π_(k,j) ^(i)[n] of the bit a prioriprobabilities previously defined, we may write:${\Pr^{i}\lbrack {{s_{k}\lbrack n\rbrack} = s} \rbrack} = {\frac{1}{2^{q}}{\prod\limits_{j = 1}^{q}\quad\{ {1 + {( {{2{\mu_{j}^{- 1}(s)}} - 1} ){\tanh( \frac{\pi_{k,j}^{i}\lbrack n\rbrack}{2} )}}} \}}}$and finally find:${{\overset{\_}{s}}_{k}^{i}\lbrack n\rbrack} = {\frac{1}{2^{q}}{\sum\limits_{s\quad{\varepsilon\mathcal{J}}}^{\quad}\quad{s \times {\prod\limits_{j = 1}^{q}\quad\{ {1 + {( {{2\quad{\mu_{j}^{- 1}(s)}} - 1} ){\tanh( \frac{\pi_{k,j}^{i}\lbrack n\rbrack}{2} )}}} \}}}}}$5.2 Sent chip MMSE estimation

From estimated symbolic data vectors s ^(i)[n], there may be created at214 (by applying to the estimates the spreading matrix W_(n) used onsending) the chip vectors estimated on each iteration i:z ^(i)[n]=W_(n) s ^(i)[n]=[ z ₁ ^(i)[n] z ₂ ^(i[n] . . . z) _(N)^(i)[n]]^(T)that constitutes the estimated matrix Z ^(i).

This is followed by processing 215 (which may comprise multiplexing,demultiplexing, chip interleaving, block division).

The processing 215 conforms to that applied on sending downstream ofspreading 108 (see any of FIGS. 3, 4, 6 and 7).

For example, if the send processing comprises simple multiplexing to theT send antennas, as shown in FIGS. 3 and 6, the processing 215 comprisesmultiplexing onto T channels (shown in FIG. 10).

For example, if the send processing comprises multiplexing 109 onto onechannel followed by chip interleaving 110 and demultiplexing (111) tothe T send antennas, as shown in FIGS. 4 and 7, the receive processing215 comprises multiplexing onto one channel, chip interleaving anddemultiplexing onto T channels (shown in FIG. 9).

Following the processing 215, there are then generated (deduced from Z^(i)) the matrices X ^(i(1)) . . . X ^(i(B)) the columns whereof are thevectors:X ^(i(b))[l]=[ X _(l) ^(i(b))[l] X ₂ ^(i(b))[l] . . . X _(T)^(i(b))[l]^(T∈□) ^(T)that are used for the linear iterative cancellation of the MAI+ISIinterference at 201.5.3 Re-establishing Orthogonality Between User Groups by Equalization tothe Chip Time

This section considers a given block of index b that was sent by theantenna t, assuming identical processing for all of them. The inventionsuggests replacing optimum detection of the chips x_(t)[l] (in the senseof the MAP criterion) by an estimate in the sense of the (biased) MMSEcriterion, derived on the basis of the sliding window model, thecomplexity of which is polynomial in the parameters of the system and nolonger exponential. On each iteration i, there is calculated at 202 afirst filter f_(t,l) ^(i)∈□^(L) ^(w) ^(R) which, on the basis of anupdated observation (covering a portion of the block) cancels theMAI+ISI interference corrupting the chip xhd t[l] and produces anevaluation {circumflex over (x)}_(t)[l] of the chips sent that minimizesthe mean square error (MSE):E[|{circumflex over (x)}_(t)[l]−X_(t)[l]|²]subject to the constraint of absence of bias.

An unconditional MSE would be preferable for reasons of complexity: thefirst filter f_(t) ^(i) is then invariant in time for the blockconcerned of the particular channel (the filter being calculated onceand for all for the processed data block b).

From the vector of the estimates of the chips on the iteration i:X ^(i) [l]=[ X ₁ ^(i) [l+L ₁ ] . . . x _(T) ^(i) [l] . . . x _(T) ^(i)[n−L ₂ −P+1]]^(T) ∈★^((L) ^(w) ^(+P−l)T)the modified version is defined at 216, including a 0 at position L₁T+t,which is used to regenerate the MAI+ISI interference 216 for the symbolx_(t)[l]:X _(t) ^(i) [l]=[ x _(l) ^(i) [l+L ₁ ] . . . x _(t+1) ^(i) [l]0 x _(t−1)^(i) [l] . . . x _(T) ^(i) [l−L ₂ −P+1]]^(T ∈□) ^((L) ^(w) ^(+P−l)T)An estimate of MAI+ISI interference is therefore regenerated at 216 bymultiplying this vector by said Sylvester matrix H (its calculation isdescribed above in section 2.2 or 2.3):H x _(t) ^(i)[l ]

The first (Wiener) filter 202 is applied to the observation vectorobtained after subtraction at 201 of the regenerated MAI+ISIinterference:{tilde over (y)} _(t) ^(i) [l]=y[l]−H x _(t) ^(i) [l]

This first filter 202 minimizes the unconditional MSE on the (biased)estimate of the chip x,[l] and may easily be derived from the orthogonalprojection theorem:f _(t) ^(i) =e _(t) ^(†) _(t) H ^(†[HΞ) _(l) ^(i) H ^(†)+σ² I ] ³¹ ¹where e_(t) is the vector of dimension (L_(w)+P−1)T having a 1 atposition L₁T+t and zeroes everywhere else and where:Ξ _(t) ^(i) □E{( x[l])( x[l])^(†}∈□) ^((L) ^(w) ^(+P−1)T×(L) ^(w)^(+P−1)T)Ξ _(t) ^(i)=diag{(σ_(x) ²−σ _(x) ^(i2))I, . . . ,(σ _(x) ²−σ _(x)^(i2))I,σ _(x) ² I(σ_(x) ²−σ _(x) ^(i2))I, . . . ,(σ _(x) ²−σ _(x)^(i2))I}with the term ox2I situated at the position L₁T+t on the diagonal and σ_(x) ^(i2) evaluated using the following estimator:$\sigma_{\overset{\_}{x}}^{i\quad 2} \approx {{\hat{\sigma}}_{\overset{\_}{x}}^{i\quad 2}\bullet\frac{1}{{TL}_{X}}{\sum\limits_{t = 1}^{T}\quad{\sum\limits_{l = 0}^{L_{x} - 1}\quad{{{\overset{\_}{x}}_{t}^{i}\lbrack l\rbrack}}^{2}}}}$

To satisfy the absence of bias constraint, the filter must be multipliedon the left by the correction factor:{e_(t) ^(†) H†[HΞ _(t) ^(i) H†+σ² I] ⁻¹ He_(t)}⁻¹

The following final expression for the filter is obtained:f _(t) ^(i) ={e _(l) ^(†H) ^(†[) HΞ _(t) ^(i) H ^(†)+σ² I] ⁻¹ He _(t)}⁻¹e _(t) ^(†) H ^(†) [HΞ _(t) ^(i) H ^(†)+σ² I] ⁻¹

Alternatively, this filter may be replaced, completely or from adifferent iteration i (i≧1), by its single user matched filter (SUMF)version, given by:f _(t) ^(i) ={e _(t) ^(†) H ^(†) He _(t)}⁻¹ −1 ]

The evaluation of the chip x,[l] then corresponds, at the output of thefirst filter 202, to:{circumflex over (x)} _(t) ^(i) [l]=f _(t) ^(i) [y[l]−H x _(t) ^(i)[l]]=x _(t) [l]+ζ _(t) ^(i) [l]

The variance of the residual MAI+ISI interference plus noise is thenequal to:σ_(ζ) _(t) ^(i2)=σ_(x) ²[(f _(t) ^(i) He _(t))⁻¹−1]and may in practice be evaluated using the following estimator:$\sigma_{\zeta_{t}}^{i\quad 2} \approx {{{\hat{\sigma}}_{\zeta_{t}}^{i\quad 2}\bullet\frac{1}{L_{X}}{\sum\limits_{l = 0}^{L_{x} - 1}\quad{{{\hat{x}}_{t}^{i}\lbrack l\rbrack}}^{2}}} - \sigma_{x}^{2}}$Other Possible Equalization Variant:

FIG. 11 b shows a variant of the first filtering 202′ and theregeneration of MAI+ISI interference 210′, to be compared with the firstfiltering 202 and the regeneration of MAI+ISI interference 210 of FIG.11 a (representing these two detection steps included in the FIG. 9 or10 scheme).

Referring to FIG. 11 b, here the first filtering 202′ is effectedupstream of the first subtraction 201 of the MAI+ISI interferenceregenerated at 210′, and not downstream thereof as is the case in FIG.11 a.

The first filter f′ used and the MAI+ISI interference reconstructionmatrix here denoted b₁′ used can be deduced trivially from the firstfilter f and the MAI+ISI interference reconstruction matrix here denotedb₁ previously calculated (see above description with reference to FIGS.9 or 10 and 11 a), from the following equation:{circumflex over (x)}=f(y−b ₁ x )=f′y −b ₁ ′ x

In order then to deduce therefrom:f′=f;b₁′=fb₁5.4 Equivalent Gaussian Multiple Access and Multi-user Detection Model

The two situations distinguished on sending (i.e. space-time(space-frequency) spreading, and time (or frequency) spreading) produce1 or T different multiple access models.

5.4.1 Space-time (or Space-frequency) Send Spreading

Referring to FIGS. 9 and 10, the chip matrices {circumflex over(X)}^(i(1)) , . . . , {circumflex over (X)}^(i(B)) are here grouped intoa single matrix {circumflex over (X)}, which in turn is reorganized,after processing 203, into a single N×L matrix {circumflex over(Z)}^(i); the processing 203 corresponds to the converse of theprocessing 215 described in section 5.2.

There is then obtained a (canonic) Gaussian equivalent multiple accessmodel of the type:{circumflex over (Z)}^(i) =X+Y ^(i) =WS+Y ^(i)

The observed chip matrix is denoted:${\hat{Z}}^{i} = {\lbrack {{{\hat{z}}^{i}\lbrack 0\rbrack}{{\hat{z}}^{i}\lbrack 1\rbrack}\quad\ldots\quad{{\hat{z}}^{i}\lbrack {L - 1} \rbrack}} \rbrack = {\begin{bmatrix}{{\hat{z}}_{1}^{i}\lbrack 0\rbrack} & {{\hat{z}}_{1}^{i}\lbrack 1\rbrack} & \cdots & {{\hat{z}}_{1}^{i}\lbrack {L - 1} \rbrack} \\{{\hat{z}}_{2}^{i}\lbrack 0\rbrack} & {{\hat{z}}_{2}^{i}\lbrack 1\rbrack} & \cdots & {{\hat{z}}_{2}^{i}\lbrack {L - 1} \rbrack} \\\vdots & \vdots & ⋰ & \vdots \\{{\hat{z}}_{N}^{i}\lbrack 0\rbrack} & {{\hat{z}}_{N}^{i}\lbrack 1\rbrack} & \cdots & {{\hat{z}}_{N}^{i}\lbrack {L - 1} \rbrack}\end{bmatrix} \in \bullet^{N \times L}}}$

The matrix of samples of noise in time is denoted:$\Upsilon^{i} = {\lbrack {{\upsilon^{i}\lbrack 0\rbrack}{\upsilon^{i}\lbrack 1\rbrack}\quad\ldots\quad{\upsilon^{i}\lbrack {L - 1} \rbrack}} \rbrack = {\begin{bmatrix}{\upsilon_{1}^{i}\lbrack 0\rbrack} & {\upsilon_{1}^{i}\lbrack 1\rbrack} & \cdots & {\upsilon_{1}^{i}\lbrack {L - 1} \rbrack} \\{\upsilon_{2}^{i}\lbrack 0\rbrack} & {\upsilon_{2}^{i}\lbrack 1\rbrack} & \cdots & {\upsilon_{2}^{i}\lbrack {L - 1} \rbrack} \\\vdots & \vdots & ⋰ & \vdots \\{\upsilon_{N}^{i}\lbrack 0\rbrack} & {\upsilon_{N}^{i}\lbrack 1\rbrack} & \cdots & {\upsilon_{N}^{i}\lbrack {L - 1} \rbrack}\end{bmatrix} \in \bullet^{N \times L}}}$

For each time n, we set:${\Xi_{\upsilon{\lbrack n\rbrack}}^{i}{\bullet E}\{ {{\upsilon^{i}\lbrack n\rbrack}{\upsilon^{i}\lbrack n\rbrack}^{\dagger}} \}} = {\begin{bmatrix}\sigma_{\upsilon_{1}{\lbrack n\rbrack}}^{i\quad 2} & \quad & \quad & \quad \\\quad & \sigma_{\upsilon_{2}{\lbrack n\rbrack}}^{i\quad 2} & \quad & \quad \\\quad & \quad & ⋰ & \quad \\\quad & \quad & \quad & \sigma_{\upsilon_{N}{\lbrack n\rbrack}}^{i\quad 2}\end{bmatrix} \in \bullet^{N \times N}}$The matrix of covariance of the residual MAI+ISI interference plus noisevectors. This is made diagonal either thanks to the chip de-interleavingincluded at 203 or the aperiodic nature of the spreading. Its diagonalelements are deduced from the variances previously estimates:{circumflex over (σ)}_(ζ) _(t) ^(i2)t=1, . . . , T

To simplify subsequent processing (MMSE multi-user detection), avariance of the noise samples that is constant for the whole of thesystem may be assumed:${{\sigma_{\upsilon_{t}{\lbrack n\rbrack}}^{i\quad 2} \approx {\hat{\sigma}}_{\upsilon}^{i\quad 2}} = {{{\frac{1}{N\quad L}{\sum\limits_{n = 0}^{L - 1}\quad{\sum\limits_{l = 1}^{N}\quad{{{\hat{z}}_{l}^{i}\lbrack n\rbrack}}^{2}}}} - {\sigma_{z}^{2}{\forall l}}} = 1}},\ldots\quad,N$

The temporal dependency is then eliminated:Ξ_(ν[n]) ^(i)=Ξ_(ν) ^(i)=σ_(v) ^(i2) I ∀n=0 , . . . ,L−15.4.1.1 Periodic Space-time (Space-frequency) send Spreading

As seen above, when the spreading is periodic, a chip interleaver (110)is used on sending, so that the processing 203 includes chipde-interleaving (see FIG. 9).

Variant 1: Overloaded Regime: MMSE Multi-user Detection

Here the optimum detection of the symbols s_(k)[n] (in the sense of theMAP criterion) is replaced by a non-biased MMSE evaluation thecomplexity whereof is polynomial in the parameters of the system and notexponential. On each iteration i, for each potential user k, there iscalculated at 204 a second filter g_(k ,n) ^(i)∈□^(N) which, on thebasis of an updated observation (relating to the column indexed n of thepreceding model), eliminates the MUI interference corrupting the symbols_(k)[n] and produces an evaluation ŝ_(k) ^(i)[n] of the sent modulateddata (or symbols) that minimizes the mean square error (MSE):E[s_(k)[n]−ŝ_(k) ^(i)[n]]subject to the constraint of the absence of bias. An unconditional MSEwould be preferable for reasons of complexity: the second filter g_(k)^(i) is then invariant in time for the block concerned of the particularchannel (i.e. calculated once and for all over the whole of the blockbeing processed).

From the vector of the estimates of the symbols at the iteration i:s ^(i)[n]=[ s ₁ ^(i)[n] s ₂ ^(i)[n]. . . s _(k) ^(i [n]]) ^(T)∈□^(K)it is possible to define at 213 the modified version, including a 0 atposition k, that is used for the regeneration 213 of the MUIinterference for the symbol s_(k)[n]:s _(k)[n]=[ s ₁ ^(i)[n] . . . s _(k−1) ^(i)[n]0 s _(k−1) ^(i)[n] . . . s_(k) ^(i)[n]]^(T)∈□^(K)

An estimate of the MUI interference is therefore regenerated at 213 bymultiplying the latter vector by the spreading matrix W used on sending:W s _(k) ^(i)[n]

The second (Wiener, biased) filter is then applied at 205 to theobservation vector obtained following subtraction 204 of thisregenerated MUI interference:{tilde over (Z)} _(k) ^(i) [n]={circumflex over (z)} ^(i) [n]−W s _(k)^(i) [n]

This second filter 205 minimizes the unconditional MSE on the estimateof the symbol s_(k)[n] and can easily be derived using the theorem oforthogonal projection:g _(k) ^(i) =e _(k) ^(†) W ^(†) [WΞ _(k) ^(i) W ^(†+σ) _(v) ^(i2) I] ⁻¹where e_(k) is the vector of dimension K have a 1 at position k andzeros everywhere else and where:Ξ_(k) ^(i) □E{(s[n]− s _(k) ^(i) [n])(s[n]− s _(k) ^(i)[n])^(†)}∈□^(K×K)Ξ_(k) ^(i)=diag{σ_(s) ²−σ _(s) _(k) ^(i2) , . . . , σ_(s) ²−σ _(s) _(k)^(i2) ,σ_(s) ² ,σ_(s) ²−σ _(s) _(k) ² , . . . , σ_(s) ^(2 −σ) _(s) _(k)^(i2)}with a, σ_(s) ² situated at the position k on the diagonal and σ _(s)^(i2) evaluated using the following estimator:$\sigma_{{\overset{\_}{s}}_{k}}^{i\quad 2} \approx {{\hat{\sigma}}_{{\overset{\_}{s}}_{k}}^{i\quad 2}\bullet\frac{1}{L}{\sum\limits_{n = 0}^{L - 1}\quad{{{\overset{\_}{s}}_{k}^{i}\lbrack n\rbrack}}^{2}}}$

To satisfy the constraint of absence of bias, the second filter must bemultiplied on the left by the correction factor:{e_(k) ^(†)W^(†)[WΞ_(k) ^(i)W^(†+σ) _(v) ^(i2)I]⁻¹We_(k)}⁻¹

The final expression for the second filter is then obtained:g _(k) ^(i) ={e _(k) ^(†) W ^(†) [WΞ _(k) ^(i) W ^(†+σ) _(v) ^(i2) I] ⁻¹We _(k}) ⁻¹ e _(k) ^(†) W ^(†) [WΞ _(k) ^(i) W ^(†)+σ_(v) ^(i2) I] ⁻¹

The evaluation of the symbol s_(k)[n] corresponds at the output of thesecond filter 205 to:ŝ _(k) ^(i) [n]=g _(k) ^(i) [{circumflex over (Z)} ^(i) [n]−W s _(k)^(i) [n]]=s _(k) [n]+ξ _(k) ^(i) [n]

The variance of the residual MUI interference plus noise term ξ_(k)^(i)[n] can be evaluated via the following estimator:$\sigma_{\xi_{k}}^{i\quad 2} \approx {{{\hat{\sigma}}_{\xi_{k}}^{i\quad 2}\bullet\frac{1}{L}{\sum\limits_{n = 0}^{L - 1}{{{\hat{s}}_{k}^{i}\lbrack n\rbrack}}^{2}}} - \sigma_{s}^{2}}$Variant 2: Overloaded Regime: SUMF (Single User Matched-Filter)Detection

In a simplified version, the second MMSE filter at 205 may be replacedfrom any iteration i by a second SUMF filter:g_(k) ^(i)={e_(k) ^(†)W^(†)We_(k)}⁻¹e_(k) ^(†)W^(†)

The following evaluation is obtained:ŝ _(k) ^(i) [n]=g _(k) ^(i) [{circumflex over (z)} ^(i) [n]−Wŝ _(k) ^(i)[n]]

This approach avoids calculating N×N inverse matrices.

Variant 3: Non-overloaded Regime

In the non-overloaded situation, we have:W^(†W=I)

Detection amounts to applying the second filter g_(k) ^(i)=e_(k)^(†)W^(†) at 205 to the observation vector.

The evaluation is then obtained directly from:ŝ_(k) ^(i)[n]=e_(k) ^(†)W^(†){circumflex over (z)}^(i)[n]5.4.1.2 Aperiodic Space-time (Space-frequency) Spreading

In this case, the processing 203 may or may not include chipde-interleaving as described with reference to FIGS. 9 and 10. The(canonic) Gaussian equivalent multiple access model is now written:{circumflex over (z)} ^(i) [n]=W _(n) s[n]+v ^(i) [n]

Only SUMF type detection is of reasonable complexity in the aperiodiccontext, and is therefore preferably used.

Variant 1: Overloaded Regime

The filter then has the following expression:g_(k) ^(i)={e_(k) ^(†)W_(n) ^(†)W_(n)e_(k)}⁻¹e_(k) ^(†)W_(n) ^(†)Variant 2: Non-overloaded Regime

The filter then has the following expression:g_(k) ^(i)=e_(k) ^(†)W_(n) ^(†)5.4.2 Time (or Frequency) Send Spreading

The chip matrices {circumflex over (X)}^(i(1)) , . . . , {circumflexover (X)}^(i(B)) are grouped into a unique matrix {circumflex over (X)}.Following the processing 203, and with reference to FIGS. 9 and 10,{circumflex over (X)} is reorganized into T S_(F)×L matrices ,{circumflex over (Z)}^(i(1)) , . . . , {circumflex over (Z)}^(i(T))corresponding to T independent (canonic) Gaussian equivalent multipleaccess models of the type:{circumflex over (Z)}^(i(t))=Z^((t))+Y^(i(t))=W^((t))S^((t))+Y^((T))

The observed chip matrix is denoted: $\quad{\quad{\quad{\begin{matrix}{{\hat{Z}}^{i{(t)}} = \lbrack {{{\hat{z}}^{i{(t)}}\lbrack 0\rbrack}{{\hat{z}}^{i{(t)}}\lbrack 1\rbrack}\quad\ldots\quad{\quad{{\hat{z}}^{i{(t)}}\lbrack {L - 1} \rbrack}}} \rbrack} \\{= {\begin{bmatrix}{{\hat{z}}_{1}^{i{(t)}}\lbrack 0\rbrack} & {{\hat{z}}_{1}^{i{(t)}}\lbrack 1\rbrack} & \cdots & {{\hat{z}}_{1}^{i{(t)}}\lbrack {L - 1} \rbrack} \\{{\hat{z}}_{2}^{i{(t)}}\lbrack 0\rbrack} & {{\hat{z}}_{2}^{i{(t)}}\lbrack 1\rbrack} & \cdots & {{\hat{z}}_{2}^{i{(t)}}\lbrack {L - 1} \rbrack} \\\vdots & \vdots & ⋰ & \vdots \\{{\hat{z}}_{S_{F}}^{i{(t)}}\lbrack 0\rbrack} & {{\hat{z}}_{S_{F}}^{i{(t)}}\lbrack 1\rbrack} & \cdots & {{\hat{z}}_{S_{F}}^{i{(t)}}\lbrack {L - 1} \rbrack}\end{bmatrix} \in \bullet^{S_{F} \times L}}}\end{matrix}\quad}}}$

The matrix of the samples of noise decorrelated in time: $\begin{matrix}{\Upsilon^{i{(t)}} = \lbrack {{\upsilon^{i{(t)}}\lbrack 0\rbrack}{\upsilon^{i{(t)}}\lbrack 1\rbrack}\quad\ldots\quad{\upsilon^{i{(t)}}\lbrack {L - 1} \rbrack}} \rbrack} \\{= {\begin{bmatrix}{\upsilon_{1}^{i{(t)}}\lbrack 0\rbrack} & {\upsilon_{1}^{i{(t)}}\lbrack 1\rbrack} & \cdots & {\upsilon_{1}^{i{(t)}}\lbrack {L - 1} \rbrack} \\{\upsilon_{2}^{i{(t)}}\lbrack 0\rbrack} & {\upsilon_{2}^{i{(t)}}\lbrack 1\rbrack} & \cdots & {\upsilon_{2}^{i{(t)}}\lbrack {L - 1} \rbrack} \\\vdots & \vdots & ⋰ & \vdots \\{\upsilon_{S_{F}}^{i{(t)}}\lbrack 0\rbrack} & {\upsilon_{S_{F}}^{i{(t)}}\lbrack 1\rbrack} & \cdots & {\upsilon_{S_{F}}^{i{(t)}}\lbrack {L - 1} \rbrack}\end{bmatrix} \in \bullet^{S_{F} \times S_{F}}}}\end{matrix}$

For each time, we set:${\Xi_{\upsilon^{(t)}{\lbrack n\rbrack}}^{i}\bullet\quad E\{ {{\upsilon^{i{(t)}}\lbrack n\rbrack}{\upsilon^{i{(t)}}\lbrack n\rbrack}^{\dagger}} \}} = {\begin{bmatrix}\sigma_{\upsilon_{1}^{(t)}{\lbrack n\rbrack}}^{i\quad 2} & \quad & \quad & \quad \\\quad & \sigma_{\upsilon_{2}^{(t)}{\lbrack n\rbrack}}^{i\quad 2} & \quad & \quad \\\quad & \quad & ⋰ & \quad \\\quad & \quad & \quad & \sigma_{\upsilon_{S_{F}}^{(t)}{\lbrack n\rbrack}}^{i\quad 2}\end{bmatrix} \in \bullet^{S_{F} \times S_{F}}}$the matrix of covariance of the residual MAI+ISI interference plus noisevectors. This is made diagonal either by the chip de-interleavingincluded in the processing 203 or by the aperiodic character of thespreading. Its diagonal elements are deduced by the variances previouslyestimated over the various blocks processed:{circumflex over (σ)}_(ζ) _(t) ^(i2)t=1 , . . . , T

To simplify subsequent processing (MMSE multi-user detection), aconstant variance of the noise samples for the whole of the system maybe assumed:${{\sigma_{\upsilon_{l}^{(t)}{\lbrack n\rbrack}}^{i\quad 2} \approx {\hat{\sigma}}_{\upsilon}^{{i{(t)}}2}} = {{{\frac{1}{{SF}\quad L}{\sum\limits_{n = 0}^{L - 1}\quad{\sum\limits_{l = 1}^{SF}\quad{{{\hat{z}}_{l}^{i{(t)}}\lbrack n\rbrack}}^{2}}}} - {\sigma_{z}^{2}{\forall l}}} = 1}},\ldots\quad,N$

The temporal dependency is then eliminated:Ξ_(ν) ^((t)) _([n]) ^(i)=Ξ_(ν) ^(i(t))=σ_(v) ^(i(t)2) I ∀n=0 , . . . ,L−1

The calculations of the filters g_(u) ^(i(t)) for each multiple accessmodel being similar to those described above, they will not be explainedhere.

5.4.2.1 Periodic Time (or Frequency) Send Spreading

As previously explained, when the spreading is periodic, a chipinterleaver (110) is used on sending, and so the processing 203 includeschip de-interleaving as described with reference to FIG. 9.

Variant 1: Overloaded Regime: MMSE Multi-user Detection

The filter then has the following expression:g _(u) ^(i(t)) ={e _(u) ^(†) [W ^((t)t) [W ^((t))Ξ_(u) ^(i) W ^((t)†) +σ_(v) ^(i2) I] ⁻¹ W ^((t)) e _(u)}⁻¹ e _(u) ^(†) W ^((t)†)σ_(u) ^(i2) I]⁻¹Variant 2: Overloaded Regime: SUMF (Single User Matched-Filter)Detection

From any iteration i, the MMSE filter may be replaced by its sub-optimumSUMF version:g_(u) ^(i(t))={e_(u) ^(†)W^((t)†)W^((t))e_(u)}⁻¹e_(u) ^(†)W^((t)†)Variant 3: Non-overloaded Regime

The filter then has the following expression:g_(u) ^(i)=e_(u) ^(†)W^(i(t))5.4.2.2 Periodic Aperiodic Time (or Frequency) Send Spreading

In this case, the processing 203 may or may not include chipde-interleaving as described with reference to FIGS. 9 and 10. The T(canonic) Gaussian equivalent multiple access models are now written:{circumflex over (Z)} ^(i(t)) [n]=W _(n) ^((t)) s ^((t)) [n]+u ^(i(t))[n]

Only SUMF-type detection is of reasonable complexity in the aperiodiccontext.

Variant 1: Overloaded Regime

The filter then has the following expression:g_(u) ^(i(t))={e_(u) ^(†)W_(n) ^((t)†)W_(n) ^((t))e_(u)}⁻¹ e _(k)^(†)W_(n) ^((t)†)Variant 2: Non-overloaded Regime

The filter then has the following expression:g_(u) ^(i(t))=e_(u) ^(†)W_(n) ^((t)†)Other Possible Equalization Variant:

Regardless of the variants explained in sections 5.4.1 and 5.4.2, thereis also a variant as to how to effect the second filtering 205′ and theMUI interference regeneration 213′ (described with reference to FIG. 12b), to be compared to the second filtering 205 and the MUI interferenceregeneration 213 of FIG. 12 a (representing these two detection stepsincluded in the FIG. 9 or 10 scheme).

Referring to FIG. 12 b, the second filtering 205′ is here effectedupstream of the second subtraction 204 of interference regenerated at213′, rather than downstream thereof as in FIG. 12 a.

The second filter g′ used and the MUI interference reconstruction matrixb₂ ′ used may be deduced trivially from the second filter g and the MUIinterference reconstruction matrix b₂ previously computed (see abovedescription with reference to FIGS. 9 or 10 and 12 a), from thefollowing condition of equality:ŝ=g({circumflex over (z)}−b ₂ s )=g′{circumflex over (z)}−b ₂ ′ s

From which we deduce:g′=g;b₂′=gb₂5.5 Exchange of Probabilistic Information with the Channel Decoder

On the basis of the output of the linear filtering 205 with K filters, qlogarithmic a posteriori probability (APP) ratios are computed at 206for each symbol, at each time n=0, . . . , L−1, for each user k=1, . . ., K. These probabilistic quantities are defined as follows:${\lambda_{k,j}^{i}\lbrack n\rbrack}{\bullet ln}\quad\frac{\Pr\lbrack {{d_{k,j}\lbrack n\rbrack} = {1 {{\hat{s}}_{k}^{i}\lbrack n\rbrack} \rbrack}} }{\Pr\lbrack {{d_{k,j}\lbrack n\rbrack} = {0 {{\hat{s}}_{k}^{i}\lbrack n\rbrack} \rbrack}} }$and are referenced Λ in FIGS. 9, 10 and 13; or:${\lambda_{k,j}^{i}\lbrack n\rbrack} = {\ln\quad\frac{\sum\limits_{d \in \quad\aleph_{j}^{(1)}}^{\quad}{\Pr\lbrack {{d_{k}\lbrack n\rbrack} = {d {{\hat{s}}_{k}^{i}\lbrack n\rbrack} \rbrack}} }}{\sum\limits_{d \in \quad\aleph_{j}^{(0)}}^{\quad}{\Pr\lbrack {{d_{k}\lbrack n\rbrack} = {d {{\hat{s}}_{k}^{i}\lbrack n\rbrack} \rbrack}} }}}$into which we introduce:z,901 _(j) ^((ε)) ={d∈F ₂ ^(q) |d _(j) =ε}

Expanding the numerator and the denominator gives:${\lambda_{k,j}^{i}\lbrack n\rbrack} = {\ln\quad\frac{\sum\limits_{d \in A_{j}^{(1)}}{{p( { {{\hat{s}}_{k}^{i}\lbrack n\rbrack} \middle| {s_{k}\lbrack n\rbrack}  = {\mu(d)}} )}{\Pr^{i}\lbrack {{d_{k}\lbrack n\rbrack} = d} \rbrack}}}{\sum\limits_{d \in A_{j}^{(0)}}{{p( { {{\hat{s}}_{k}^{i}\lbrack n\rbrack} \middle| {s_{k}\lbrack n\rbrack}  = {\mu(d)}} )}{\Pr^{i}\lbrack {{d_{k}\lbrack n\rbrack} = d} \rbrack}}}}$

The likelihoods are expressed as follows:${p( { {{\hat{s}}_{k}^{i}\lbrack n\rbrack} \middle| {s_{k}\lbrack n\rbrack}  = {\mu(d)}} )} \propto {\exp( {- \frac{{{{{\hat{s}}_{k}^{i}\lbrack n\rbrack} - {\mu(d)}}}^{2}}{{\hat{\sigma}}_{\zeta_{k}}^{i\quad 2}}} )}$

On each iteration i, a priori information on the bits of the varioussymbols coming from the channel decoders 209 is available and usable inthe form of logarithmic APP ratios introduced beforehand and theexpression for which is:${\pi_{k,j}^{i}\lbrack n\rbrack}{\bullet ln}\frac{\Pr^{i}\lbrack {{d_{k,j}\lbrack n\rbrack} = 1} \rbrack}{\Pr^{i}\lbrack {{d_{k,j}\lbrack n\rbrack} = 0} \rbrack}$

Assuming space-time interleaving of sufficiently great depth, we maywrite:${\Pr^{i}\lbrack {{d_{k}\lbrack n\rbrack} = d} \rbrack} \approx {\prod\limits_{j = 1}^{q}{\Pr^{i}\lbrack {{d_{k,j}\lbrack n\rbrack} = d_{j}} \rbrack}} \propto {\prod\limits_{j = 1}^{q}\{ {1 - {( {{2d_{j}} - 1} ){\tanh( \frac{\pi_{k,j}^{i}\lbrack n\rbrack}{2} )}}} \}}$

The extrinsic information on each bit delivered by weighted outputdemodulators 206 intended for the channel decoder 209 is then found at207 from the equation:ξ_(k,j) ^(i)[n]□λ_(k,j) ^(i)[n]−π_(k,j) ^(i)[n]

All the bit extrinsic information logarithmic ratios for all the blocksare then collected and properly multiplexed and de-interleaved at 205,to be sent to the channel decoder 209.

This decoder sees a unique vector φ^(i)∈□^(n) ^(o) made up of N_(o) bitintrinsic probability logarithmic ratios (one for each bit of the codeword v). Decoding 206 then uses an algorithm such as the flexible outputViterbi algorithm to deliver the logarithm λ of a ratio of informationAPP to sent modulated data (or symbols) bits.

This logarithm λ is then the basis on which are computed at 210 a and210 b the bit extrinsic information logarithmic ratios, formally defined∀l=1, . . . , N_(o) as follows:$\xi_{l}^{i}{\bullet ln}\quad\frac{\Pr^{i}\lbrack {{v_{l} =  1 \middle| C_{o} },{\varphi^{i}/\{ \varphi_{l}^{i} \}}} \rbrack}{\Pr^{i}\lbrack {{v_{l} =  0 \middle| C_{o} },{\varphi^{i}/\{ \varphi_{l}^{i} \}}} \rbrack}$

The code word extrinsic information logarithmic ratios {ξ_(l) ^(i) }calculated in the iteration i are similar, after bit interleaving anddemultiplexing 208 a and 208 b, to the symbol bit APP logarithmic ratios{πhd k,j^(i +1)[n]) } on the next iteration.

Reception in accordance with the invention refers not only to a methodfor implementing it but also to the system for executing it and anytransmission system incorporating that reception system.

1. A reception method for communication over frequency-selectivechannels with a plurality of send antennas and a plurality of receiveantennas, characterized in that said reception method is adapted toprocess data received by the receive antennas that, on sending, wassuccessively: (A) modulated onto K channels, the number K being strictlygreater than the number T of send antennas; (B) spread with an N×Kperiodic spreading matrix (W) or an N×K aperiodic spreading matrix(W_(n)) where N is strictly greater than T, over the K-dimensionalvectors of the modulated data; (C) processed to be transmitted from theT send antennas; and in that the reception method uses iteratively forthis purpose: first filtering by means of T linear filters (202, 202′)adapted to process the received data, where applicable after subtractionof a multi-antenna interference (MAI) and intersymbol interference (ISI)estimate, to generate an evaluation ({circumflex over (x)}) of the chipssent after the spreading of the step (B), this first filtering takingaccount in particular of the spatial diversity of the plurality ofreceive antennas; before or after said first filtering, firstsubtracting of interference (201) using an estimate of multi-antennainterference (MAI) and intersymbol interference (ISI) previouslyregenerated from information computed on the basis of an evaluation (ŝ)of the sent modulated data generated by a previous filtering operation;processing (203) that is the converse of that of the sending step (C),using a reorganization of the chips ({circumflex over (x)}) evaluatedpreviously; second filtering by means of K linear filters (205, 205′)adapted to process the evaluation of the chips ({circumflex over (x)})sent obtained in this way, where appropriate after subtracting anestimate of multi-user interference (MUI), to generate an evaluation (ŝ)of the sent modulated data before the spreading of the step (B), thissecond filtering taking account in particular of the spatial diversityof the plurality of receive antennas; before or after said secondfiltering, second substraction of interference (204) that uses an MUIinterference estimate previously regenerated from information calculatedon the basis of an evaluation (ŝ) of the sent modulated data generatedby previous filtering; processing to generate an MAI+ISI interferenceestimate and an MUI interference estimate from the data received, on thebasis of information calculated on the basis of said evaluation (ŝ) ofthe sent modulated data, the MAI+ISI interference estimate and the MUIinterference estimate being then sent recursively to the next firstsubtraction (201) and the next second subtraction (204), respectively.2. A reception method according to claim 1, characterized in that thesend spreading of the step (B) is effected with K strictly greater thanN.
 3. A method according to claim 1, characterized in that the receptionmethod is adapted to process data that, on sending, was spread duringthe step (B), independently for each antenna and with a number ofchannels per antenna strictly greater than 1, the spreading matrix (W,W_(n)) is a diagonal block matrix with a number of blocks equal to thenumber of antennas, and the blocks are constructed from N/T orthogonalcodes.
 4. A method according to claim 1, characterized in that thereception method is adapted to process data that, on sending, was spreadduring the step (B) by means of a spreading full matrix (W, W_(n))constructed from N orthogonal codes.
 5. A reception method according toclaim 1, characterized in that the T first filters are derived using thecriterion of minimizing the mean square error (MMSE), the T firstfilters being invariant in time for a given channel.
 6. A receptionmethod according to claim 1, characterized in that the T first filtersare matched filters (commonly called single-user matched filters(SUMF)).
 7. A reception method according to claim 1, characterized inthat the T first filters are first derived in accordance with thecriterion of minimizing the mean square error (MMSE), and then becomematched filters (commonly called single-user matched filters (SUMF))from a given iteration.
 8. A reception method according to claim 1,characterized in that the spreading of the send step (B) is effectedperiodically, the step (C) comprises chip interleaving, the K secondfilters are derived in accordance with the unconditional criterion ofminimizing the mean square error, and the K first filters are invariantin time for a given channel.
 9. A reception method according to claim 1,characterized in that the K second filters are matched filters commonlycalled single user matched filters (SUMF).
 10. A reception methodaccording to claim 1, characterized in that the spreading of the sendingstep (B) is effected periodically, the step (C) comprises chipinterleaving, and the K second filters are first derived in accordancewith the unconditional criterion of minimizing the mean square error(the K second filters thus being invariant in time for a given channel),and then become K matched filters (commonly called single-user matchedfilters (SUMF)) from a given iteration.
 11. A reception method accordingto claim 1, characterized in that the T first filters take account inparticular of the spatial diversity of the plurality of receive antennasby maximizing the signal-to-noise ratio (SNR) after filtering (202). 12.A reception method according to claim 1, characterized in that the firstand/or second filters are computed using sliding windows.
 13. Areception method according to claim 1, characterized in that thespreading of the sending step (B) is effected aperiodically and theprocessing of the sending step (C) comprises multiplexing onto the Tsend antennas without interleaving, and in that said converse processing(203) on reception then comprises demultiplexing onto N channels.
 14. Areception method according to claim 1, characterized in that theprocessing of the sending step (C) comprises multiplexing onto onechannel, chip interleaving and then demultiplexing onto the T sendantennas, and in that said converse processing on reception thencomprises multiplexing onto one channel, chip de-interleaving, and thendemultiplexing onto N channels.
 15. A reception method according toclaim 1, characterized in that, on sending, the data was coded beforethe step (A), and in that, on reception, said processing to generateinterference estimates uses: weighted output processing (206) processingthe evaluation (ŝ) of the sent modulated data and generating modulateddata bit probabilistic information usable for decoding; decoding (209)to generate a probabilistic quantity (λ) from said probabilisticinformation; MUI interference regeneration (213, 213′) generating an MUIinterference estimate on the basis of this probabilistic quantity (λ)this interference estimate then being sent recursively to the nextsecond subtraction step (204); MAI+ISI interference regeneration (216,216′) to generate an MAI+ISI interference estimate on the basis of theprobabilistic quantity (λ) and by means of processing (215) conformingto that of the step (C), this interference estimate then being sentrecursively to the next first subtraction step (201).
 16. A receptionmethod according to claim 15, characterized in that the regeneration ofMAI+ISI and MUI interference generates interference estimates from anestimate ( S) of the sent modulated data, which estimate ( S) iscomputed (212) in the sense of the criterion of minimizing the meansquare error (MMSE) on the basis of extrinsic information (ξ) that is afunction of bits sent previously available after decoding (209).
 17. Areception method according to claim 1, characterized in that, onsending, the data was coded and interleaved before the step (A) and, onreception, said processing to generate interference estimates uses:weighted output processing (206) based on the evaluation of the sentmodulated data ( S) and decoding statistics (Π) resulting from decoding(209) to generate a statistic (Λ) per modulated data bit;de-interleaving (208) at the extrinsic statistics bit level (Ξ) foundfrom the probabilistic quantity (Λ) generated previously; weighted inputand output decoding (209) on the basis of the data de-interleaved inthis way (φ) to produce a probabilistic quantity (λ) over all of thebits; interleaving (211 a-211 b) at the extrinsic statistics bit level(ξ) found from the probabilistic quantity (λ), the new statistics (Π)thus interleaved then being sent recursively to the next step (206) ofweighted output processing; regenerating MUI interference (210, 210′) togenerate an MUI interference estimate on the basis of an estimate ( S)of the sent modulated data computed (212) in the sense of the criterionof minimizing the mean square error (MMSE) from said new interleavedstatistics (Π), which MUI interference estimate is then sent recursivelyto the next second subtraction step (204); MAI+ISI interferenceregeneration (216, 216′) to generate an MAI+ISI interference estimate onthe basis of the same estimate ( S) of the sent modulated data by meansof processing (215) conforming to that of step (C), this interferenceestimate then being sent recursively to the next first subtraction(201).
 18. A reception method according to claim 15, characterized inthat said probabilistic quantity (λ) after coding (209) is the logarithmof a ratio of modulated data bit information a priori probabilities. 19.A reception method according to claim 18, characterized in that decoding(209) computes said probabilistic quantity (λ) by means of a Viterbialgorithm with weighted inputs and outputs.
 20. A reception methodaccording to claim 1, characterized in that the spreading of the sendingstep (B) is effected in the frequency domain and transmission beforereception is of the multicarrier type.
 21. A reception method accordingto claim 1, characterized in that the spreading of the sending step (B)is effected in the time domain and the transmission before reception isof the single-carrier type.
 22. A transmission system, characterized inthat it comprises: a sending system comprising a plurality of sendantennas and adapted to modulate onto K channels, the number K beingstrictly greater than the number T of send antennas, and to spread withan N×K periodic spreading matrix (W) or an N×K aperiodic spreadingmatrix (W_(n)) where N is strictly greater than T, over theK-dimensional vectors of the modulated data; a frequency-selectivetransmission channel; a reception system comprising a plurality ofreceive antennas and adapted to implement a reception method accordingto claim.
 23. A reception system for communication overfrequency-selective channels with a plurality of send antennas and aplurality of receive antennas, characterized in that the system isadapted to process data received via the receive antennas that, onsending, was successively: (A) modulated onto K channels, the number Kbeing strictly greater than the number T of send antennas; (B) spread inthe time or frequency with an N×K periodic spreading matrix (W) or anN×K aperiodic spreading matrix (W_(n)) where N is strictly greater thanT, over the K-dimensional vectors of the modulated data; (C) processedto be transmitted from the T send antennas; and in that the systemcomprises for this purpose: T first linear filters (202, 202′) adaptedto process the received data, where applicable after subtraction of amulti-antenna interference (MAI) and intersymbol interference (ISI)estimate, to generate an evaluation ({circumflex over (x)}) of the chipssent after the spreading of the step (B), this filter taking account inparticular of the spatial diversity of the plurality of receiveantennas; upstream or downstream of said T first filters, a firstinterference subtractor that uses an estimate of multi-antennainterference (MAI) and intersymbol interference (ISI) previouslyregenerated from information computed on the basis of an evaluation (ŝ)of the sent modulated data generated by previous filtering; processingmeans (203) adapted to execute processing that is the converse of thatof the sending step (C), using a reorganization of the chips({circumflex over (x)}) evaluated previously; K second linear filters(205, 205′) adapted to process the evaluation of the chips ({circumflexover (x)}) sent obtained in this way, where appropriate aftersubtracting an estimate of multi-user interference (MUI), to generate anevaluation (ŝ) of the sent modulated data before the spreading of thestep (B), this second filtering taking account in particular of thespatial diversity of the plurality of receive antennas; upstream ordownstream of said K second filters, a second interference subtractor(204) that uses an MUI interference estimate previously regenerated frominformation calculated on the basis of an evaluation (ŝ) of the sentmodulated data generated by previous filtering; processing means forgenerating an MAI+ISI interference estimate and an MUI interferenceestimate from the data received, on the basis of information calculatedon the basis of said evaluation (ŝ) of the sent modulated data, theMAI+ISI interference estimate and the MUI interference estimate beingthen sent recursively to the next first subtraction (201) and the nextsecond subtraction (204), respectively, these various elements of thereception system being adapted to be used iteratively.
 24. A receptionsystem according to claim 23, characterized in that the T first filtersare derived using the criterion of minimizing the mean square area(MMSE).
 25. A reception system according to claim 23, characterized inthat the T first filters are matched filters commonly called single usermatched filters (SUMF).
 26. A reception system according to claim 23,characterized in that the T first filters are first derived inaccordance with the criterion of minimizing the mean square error (MMSE)and then from a given iteration become T matched filters commonly calledsingle user matched filters (SUMF).
 27. A reception system according toclaim 23, characterized in that the spreading of the sending step (B) iseffected periodically, the step (C) comprises chip interleaving, and theK second filters are derived in accordance with the unconditionalcriterion of minimizing the mean square error, the K second filtersbeing invariant in time for a given channel.
 28. A reception systemaccording to claim 23, characterized in that the K second filters arematched filters (commonly called single-user matched filters (SUMF)).29. A reception system according to claim 23, characterized in thatspreading of the sending step (B) is effected periodically, the step (C)comprises chip interleaving, and the K second filters are first derivedin accordance with the unconditional criterion of minimizing the meansquare error (the K second filters being then invariant in time for agiven channel), and then become K matched filters (commonly calledsingle-user matched filters (SUMF)) from a given iteration.
 30. Areception system according to claim 23, characterized in that spreadingof the sending step (B) is effected aperiodically and the processing ofthe sending step (C) comprises multiplexing onto the T send antennas,and in that the processing means (203) adapted to execute processingthat is the converse of that of the sending step (C) then comprise ademultiplexer onto N channels.
 31. A reception system according to claim23, characterized in that the processing of the sending step (C)comprises multiplexing onto one channel, chip interleaving and thendemultiplexing onto the T send antennas, and in that the processingmeans (203) adapted to execute processing that is the converse of thatof the sending step (C) then comprise a multiplexer onto one channel, achip de-interleaver and then a demultiplexer onto N channels.
 32. Areception system according to claim 23, characterized in that, onsending, the data was coded before the step (A) and in that, onreception, said processing means for generating interference estimatescomprise: weighted output processing means (206) for processing theevaluation (ŝ) of the sent modulated data and generating modulated databit probabilistic information usable by a decoder; a decoder (209) forgenerating a probabilistic quantity (λ) from said probabilisticinformation; an MUI interference regenerator (213, 213′) for generatingan MUI interference estimate based on this probabilistic quantity (λ),this interference estimate then being sent recursively to the secondsubtractor (204); an MAI+ISI interference regenerator (216, 216′) forgenerating an MAI+ISI interference estimate on the basis of theprobabilistic quantity (λ) by means of processing (215) conforming tothat of step (C), this interference estimate then being sent recursivelyto the first subtractor (201).
 33. A reception system according to claim23, characterized in that, on sending, the data is coded and interleavedbefore the step (A) and in that said processing means for generatinginterference estimates on reception comprise: weighted output processingmeans (206) for generating a statistic (Λ) for each modulated data bitfrom the evaluation (Ŝ) of the sent modulated data and decodingstatistics (Π) from a decoder (209); a de-interleaver (208) at the bitlevel of extrinsic statistics (Ξ) found from the probabilistic quantity(Λ) generated previously; a one weighted input and output decoder (209)for producing from data de-interleaved in this way (φ) producing aprobabilistic quantity (λ) over all of the bits; an interleaver (211a-211 b) at the bit level of extrinsic statistics (ζ) found from theprobabilistic quantity (λ), new statistics (Π) thus interleaved beingthen sent recursively to the weighted output processing means (206); anMUI interference regenerator (210, 210′) for generating an MUIinterference estimate on the basis of an estimate ( S) of the sentmodulated data, which was computed (212) in the sense of the criterionof minimizing the mean square error (MMSE) from said new interleavedstatistics (Π), which MU interference estimate is then sent recursivelyto the second subtractor (204); MAI+ISI interference regeneration (216,216′) to generate an MAI+ISI interference estimate on the basis of thesame estimate ( S) of the sent modulated data by means of processing(215) conforming to that of step (C), this interference estimate thenbeing sent recursively to the first subtractor (201).